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Foundations for a SelfReflective, ContextAware Semantic Representation of Mathematical Specifications
"... 5.2 The representation of informal mathematical text....... 83 5.3 The representation of optimization problems.......... 86 ..."
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5.2 The representation of informal mathematical text....... 83 5.3 The representation of optimization problems.......... 86
DynGenPar – A Dynamic Generalized Parser for Common Mathematical Language ⋆
"... Abstract. This paper introduces a dynamic generalized parser aimed primarily at common natural mathematical language. Our algorithm combines the efficiency of GLR parsing, the dynamic extensibility of tableless approaches and the expressiveness of extended contextfree grammars such as parallel mult ..."
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Abstract. This paper introduces a dynamic generalized parser aimed primarily at common natural mathematical language. Our algorithm combines the efficiency of GLR parsing, the dynamic extensibility of tableless approaches and the expressiveness of extended contextfree grammars such as parallel multiple contextfree grammars (PMCFGs). In particular, it supports efficient dynamic rule additions to the grammar at any moment. The algorithm is designed in a fully incremental way, allowing to resume parsing with additional tokens without restarting the parse process, and can predict possible next tokens. Additionally, we handle constraints on the token following a rule. This allows for grammatically correct English indefinite articles when working with word tokens. It can also represent typical operations for scannerless parsing such as maximal matches when working with character tokens. Our longterm goal is to computerize a large library of existing mathematical knowledge using the new parser, starting from natural language input as found in textbooks or in the papers collected by the digital mathematical library (DML) projects around the world. In this paper, we present the algorithmic ideas behind our approach, give a short overview of the implementation, and present some efficiency results. The new parser is available at
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"... DISSERTATION Titel der Dissertation Foundations for a selfreflective, contextaware semantic representation of mathematical specifications ..."
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DISSERTATION Titel der Dissertation Foundations for a selfreflective, contextaware semantic representation of mathematical specifications
Chapter 3 Towards a Selfreflective, Contextaware Semantic Representation of Mathematical Specifications
"... Abstract We discuss a framework for the representation and processing of mathematics developed within and for the MOSMATH project. The MOSMATH project aims to create a software system that is able to translate optimization problems from an almost natural language to the algebraic modeling language A ..."
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Abstract We discuss a framework for the representation and processing of mathematics developed within and for the MOSMATH project. The MOSMATH project aims to create a software system that is able to translate optimization problems from an almost natural language to the algebraic modeling language AMPL. As part of a greater vision (the FMathL project), this framework is designed both to serve the optimizationoriented MOSMATH project, and to provide a basis for the much more general FMathL project. We introduce the semantic memory, a data structure to represent semantic information, a type system to define and assign types to data, and the semantic virtual machine (SVM), a low level, Turingcomplete programming system that processes data represented in the semantic memory. Two features that set our approach apart from other frameworks are the possibility to reflect every major part of the system within the system itself, and the emphasis on the contextawareness of mathematics. Arguments are given why this framework appears to be well suited for the representation and processing of arbitrary mathematics. It is discussed which mathematical content the framework is currently able to represent and interface. Acknowledgments.